Interactions in Sphere Packings

Abstract

Ordered Colloids / Bacterial Patterns / Sphere Packing / Thermodynamic Stability / InteractionsThe circle packings including non-periodic packings and 41 homogeneous sphere packings with 4 ≤ T 1 ≤ 12 contacts are analyzed for physical and thermodynamic stability. The two-and three-dimensional structures A x B y can be characterized by the numbers T 1 and T 2 of nearest and next-nearest neighbors of the same kind. A small number of structures at the border of the T 1 , T 2 structure maps is stabilized by enthalpy compared to an increased number of entropy stabilized structures. The self-coordination numbers T i correspond to the numbers of contacts for sphere packing.

Characteristic Lattice Complexes

“…Adsorbed atoms A on metal surfaces and different inorganic structures A x B y will follow as examples for 2D and 3D structures. The self-coordination numbers of A and B can frequently be correlated with attractive or repulsive interactions of the Ising model [2,4]. Small numbers of nearest neighbors T 1 indicate repulsive A-A interactions, small numbers T 2 of next-nearest neighbors attractive interactions, as will be outlined for 1D ordering in the next section.…”